We have discovered both a red and a blue subpopulation of ultra-compact dwarf (UCD) galaxy candidates in the Coma galaxy cluster. We analyzed deep F475W (Sloan g) and F814W (I) Hubble Space Telescope images obtained with the Advanced Camera for Surveys Wide Field Channel as part of the Coma Cluster Treasury Survey and have fitted the light profiles of ~5000 point-like sources in the vicinity of NGC 4874, one of the two central dominant galaxies of the Coma Cluster. Although almost all of these sources are globular clusters that remain unresolved, we found that 52 objects have effective radii between ~10 and 66 pc, in the range spanned by dwarf globular transition objects (DGTOs) and UCDs. Of these 52 compact objects, 25 are brighter than MV ~ –11 mag, a magnitude conventionally thought to separate UCDs and globular clusters. The UCD/DGTO candidates have the same color and luminosity distribution as the most luminous globular clusters within the red and blue subpopulations of the immensely rich NGC 4874 globular cluster system. Unlike standard globular clusters, blue and red UCD/DGTO subpopulations have the same median effective radius. The spatial distribution of UCD/DGTO candidates reveals that they congregate toward NGC 4874 and are not uniformly distributed. We find a relative deficit of UCD/DGTOs compared with globular clusters in the inner 15 kpc around NGC 4874; however, at larger radii UCD/DGTO and globular clusters follow the same spatial distribution.